Topic 8: Gravitation

Source: Conceptual Physics textbook, lab book and CPO textbook and lab book

Types of Materials: Textbooks, lab books, worksheets, demonstrations/activities, vectors and

websites, and good stories

Building on: After studying dynamics and learning how force affects motion, the

concept of gravitational force fields is introduced, such as the force field

around the earth. The world was nicely introduced to force fields in the

first Star Wars movie in the late 1970’s. Acceleration of gravity (9.8

m/s/s) could have been done during dynamics or at this time, which is

where I am placing it to show the “downward vector nature” of this topic.

Following the sequence of topics presented thus far, using centripetal

force, some algebra and a new topic of the Universal Law of Gravitation,

students can understand satellite motion as well as calculate, if one

desires, satellite speed, orbit radius, and the acceleration of gravity at all

points in space. Furthermore, using energy principles, the student can

understand, and even calculate, escape velocity from earth, and bound and

unbound satellite orbits.

Links to Physics: As mentioned in the “building on” above section, satellite motion is a

natural follow-up to studying gravitation. Gravitation plays a direct role in

friction as previously presented in kinematics. Recall that friction is

directly proportional to the normal force pressing two surfaces together,

which is often gravity. When gravity is considered for forces between

atomic particles, we see it plays a very small role since it is so small

compared to the other force laws of nature. So, on the nuclear and atomic

level, gravity is there but it isn’t much of a factor. Gravitation plays an

important role in planetary motion, space travel, movement within solar

systems of moons and asteroids and the holding of solar systems together,

and the formation of comets, planets and asteroids. Let’s not forget the

formation of stars and galaxies within the universe.

Links to Chemistry: Spectrum analysis of stars can give us the information needed to

determine their chemical make-up. Meteorites that land on earth can be

chemically analyzed to determine their make-up and piece together ideas

on the formation of the universe. Our moon samples taken from the moon

give scientists ideas about the formation of our solar system. Due to the

small effect of gravity on atomic and nuclear forces, gravity in chemistry

is no real factor.

Links to Biology: NASA astronauts have done science (including biology) experiments in

non-gravity conditions and compared them to on earth situations. On

earth, crystals can be grown, but 0-g conditions produce better results. In

1991, the STS-40 crew of the Space Shuttle Columbia began an exciting

mission to understand how living things function in the microgravity

environment of Earth’s orbit. Experiments were done on jellyfish ephyrae

and their gravity receptors. Also, experiments on human systems including

cardiovascular/cardiopulmonary, homological, muscular, skeletal,

vestibular, immune and renal-endocrine were performed and compared to

earth (gravity) functions.

Materials:

(a) Hewitt

2. Lab 36 – Acceleration of Free Fall

3. Lab 37 – Computerized Gravity

4. Lab 38 – Apparent Weightlessness

(b) Hsu*

(c) Mine

Measure “g”

(d) Worksheet

Gravitational Field

(e) Demonstration

Up and Down “g”

(f) Videos and Websites

1. The g-Force Experiment

Funderstanding & Question 3D Coaster Lab Sim (Shockwave/Java)

2. http://www.space.com/businesstechnology/technology/anti_grav_000928.html

(This site discusses work underway on creating an anti-gravity device.)

3. http://www.sciencedaily.com/release/2006/03/06032222521.htm

(This site discusses an 18-month gravitational-wave search by a NASA-funded

project.)

4. http://www.space.com/scienceastronomy/equator_bulge_020801.html)

(This site explores the Earth’s gravitational shift resulting from the bulging of the

equator.)

(g) Good Stories

1. Johannes Kepler – The Father of Sci-Fi

2. Johannes Kepler – Amazing Accomplishments

3. Tycho’s Knows

4. Tycho’s Pet Moose

Topic 8: Lab – Measuring “g”

Purpose: To measure the acceleration due to gravity at the earth’s surface conceptually or

numerically.

Theory: Many authors have written fine labs on finding “g.” Some approaches include:

dropping an object from a tall location and measuring the distance of drop and the

time of drop and then using a formula to find “g”; drop an object past sensors that

start and stop time on a clock—this can be read by a computer to result in great

times; use photography or a spark timer to obtain the position of an object at

several times. The electronic spark timer sold by most science supply company’s

works great and I have used it often. No friction (except air) gives the great result,

however, if cost, storage, and being very heavy are an issue to you, then here is an

alternative. This setup is easy to assemble, inexpensive, easy to store, yet use the

same “physics thinking” as the standard spark timer.

Setup:

Hand

1.5 m Ticker Tape

About 1.5 m

Mechanical Spark Timer

Weight

Power Wires

About 1.5 m

Padded Bucket

Procedure:

1. Set up a reliable mechanical spark timer (hopefully the timer I referred to in Topic 3 will

soon be available) about 1.5 m above the floor.

(a) Attach the long electrical connection to a power supply.

(b) Test and make adjustments to the timer to obtain dark consistent dots on the paper

tape.

2. If you want a value for “g,” the timer must be calibrated:

(a) Pull a ticker tape through the vibrating timer for say 3 s and count the dots. Calibrate:

Example – In 3 s (stop watch) you get 301 dots or 300 intervals. Thus, 3 s/300 spaces

= 0.01 s/space.

(b) A more convenient and accurate method is to use a strobe light. If you have calibrated

one, the time = 1/strobe frequency.

If you want to show “g” is constant, but without determining its value, you can make up a

time like in the days of PSSC physics. Call the interval a “tick” (or tock if you prefer).

Pretend that 10 spaces equal 0.1 s. The final graphs for (a) or (b) the “tick” time approach

will all be an angled straight line when you construct an average velocity vs. time graph.

This will show that “g” is constant at 9.8 m/s/s or just constant.

3. Tape a weight (about 500 g) to the timer tape and thread through the timer.

4. With the timer operating, drop from rest the weight and attached tape with your grip at

the top of the tape into the padded bucket.

5. On the tape, mark off equal time intervals (equal number of spaces) that is

mathematically convenient or just convenient if you are just showing a constant “g.” You

should have five or more intervals to see the trend on the graph. Be sure not to include

any data points at the very beginning to ensure free fall is occurring or at the very end in

case the weight is in the bucket.

6. Record the length of the first interval in the table. Repeat for the other intervals. Record

the same interval time next to each interval distance in the table. Divide the interval

distance by the interval time and record as the average interval velocity. Make a new total

time column in the table.

Interval Distance

(m)

Interval Time

(s or tick)

Average Interval Velocity

(m/s or m/tick)

Total Time

(s or tick)

7. Plot an average interval velocity vs. total time graph. Even though the data plot will not

be plotted at the correct real total time, it doesn’t matter since the average velocity vs.

total time graph is equal to g = !v / !t, so the CHANGE in time is what counts which

will be correct.

8. Take the slope of this graph: (!v / !t), which will be the average acceleration caused by

gravity.

Questions:

1. What is the direction of acceleration caused by gravity?

2. Is g a scalar or vector?

3. Is g a constant or does it vary?

4. What is the value of g at the earth’s surface?

5. What ways do you have to improve on the outcome of the data?

Topic 8: “g” Lab Answer Sheet – Sample Data Below

Interval Distance

(m)

Interval Time

(s or tick)

Average Interval Velocity

(m/s or m/tick)

Total Time

(s or tick)

0.049 m

0.1 s

0.49 m/s

0.1 s

0.147

0.1

1.47

0.2

0.245

0.1

2.45

0.3

0.343

0.1

3.43

0.4

0.441

0.1

4.41

0.5

0.049 m 0.147 m 0.245 m 0.343 m 0.441 m

Average Interval Velocity vs. Total Time

5 m/s

o

4

o

3

v o 2

o

1

o

0

0.0 0.1 0.2 0.3 0.4 0.5 s

t

g = !v / !t

g = (4.41 - 0.49 m/s) / (0.5 - 0.1 s) = 9.8 m/s2 Slope from graph

Questions:

1. Direction of acceleration caused by gravity is DOWN; “g” is .

2. Vector (down)

3. Constant (Slope of graph is the same—constant.)

4. 9.8 m/s2 if real distance and time are used.

5. Improve measurements of time and distance. (Use electronic spark timer instead of

mechanical timer.)

Topic 8: Worksheet on Gravitation

(A) Gravitational Fields

In nature, one mathematical relationship exists in several situations. That relationship is

called the inverse square law, and it works for gravity and other situations where something

spreads out from a point in a radial direction or out from a center point. The spokes of a

bicycle wheel illustrate this idea in two dimensions. Gravitational fields behave like spokes

but are in three dimensions.

A visual example of this law appears below for a fictitious example used in a high school

physics program called PSSC (Physical Science Study Committee) physics.

Visual: Imagine a liquid butter gun capable of shooting a uniform mist from a square

nozzle located in an antigravity chamber (sound silly?). The butter would travel

through the chamber in straight lines (no gravity).

0 1’ 2’ 3’

Now imagine placing one slice of bread at 1 foot in front of the nozzle. With a squeeze of

the butter gun you find the square-shaped spray covers perfectly.

What would happen to the spray pattern if you moved to 2 feet from the nozzle? How many

pieces of bread would be uniformly covered at 2 feet?

(a) _______________________________ (b) _______________________________

If you wrote two slices, you would be incorrect since the butter spreads out up and down

but also in and out of the sketch.

The answer is four slices (2 times taller x 2 times deep = 4).

At 2 feet, what amount of butter covers each slice compared to 1 foot?

_________________________________________________________________________

What correct math relationship exists between distance and the amount of butter per slice

(consider as distance increases, the amount of butter per slice decreases)? Be careful.

_________________________________________________________________________

At 3 feet, what amount of butter per slice covers one slice of bread compared to 1 foot?

_________________________________________________________________________

Now, let’s show the connection between the above example and GRAVITY. This sketch

shows the GRAVITATIONAL FORCE FIELD around a mass in two dimensions.

C •

•

D

A • • B

Sketch X

Mass

Points A and B are the same distance from the center of the mass. Point C is twice the

distance to the center of mass and point D is four times the distance as A and B.

Questions?

1. How does the force of gravity on a mass compare at points A and B?

_____________________________________________________________________

2. How does the force of gravity on a mass at C compare to point A?

______________________________________________________________________

3. How does the force of gravity on a mass at D compare to A?

______________________________________________________________________

From dynamics, F = m a. The force of gravity on a mass created by a second mass is

F = Fs = weight (call it w).

4. If a mass is dropped from point A, which way does it fall?

______________________________________________________________________

5. If a mass is dropped from point B, which way does it fall?

______________________________________________________________________

6. What would you call the acceleration on the mass at point A?

______________________________________________________________________

7. Using symbols, what is the math relationship between the weight and mass and

acceleration of a body?

______________________________________________________________________

8. Sketch weight vectors to scale on sketch X.

(B) Acceleration of Gravity at Different Locations

When gravitational force field lines (vectors) are close together, that indicates the strength

(force/mass) is larger (g = F/m).

This example shows force field 1 and force field 2 with point X between the lines.

1 X o F 2 X o F

Which field is stronger? By looking at both sketches, 1 and 2, we see field 2 is stronger

because the gravitation force field lines are closer together.

Also, the gravitational force field obeys the inverse square law as decreased in (A), so

F ! 1/R2. So, if R is doubled, F is !

2 or " as great; if R is tripled, F is 1/3

2 or 1/9 as great.

Look at sketch X in (A) and compare the:

(a) Force field of (B) to (A):

______________________________________________________________________

(b) Force field of C compared to A:

______________________________________________________________________

(c) Force field of D compared to A:

______________________________________________________________________

Would the force field ever go to zero if a body goes far enough from the central mass?

_________________________________________________________________________

What do you think happens to the force field inside the body?

_________________________________________________________________________

_________________________________________________________________________

(C) The Universal Law of Gravitation

Sir Isaac Newton is said to have watched an apple fall from a tree and arrive at the idea that

the same force should be present on the earth from the apple as that of the earth on the

apple. In other words, any two bodies in the universe attract each other with the same force,

but in the opposite direction (body 1 attract body 2 and body 2 equally attracts body 1, but

in the opposite direction). This is the universal law of gravitation without the math. Some

everyday examples: dog attracts flea, flea attracts dog: chair attracts desk, desk attracts

chair.

Furthermore, Newton arrived at a formula (not derived here) that states:

Fg = G(m1m2)

R2

which includes the inverse square law. Fg is the force of gravity, m1 and m2 are the two

masses and R is the separation between their centers. G is the proportionality constant and

m is mass in (kg), R is separation in (m), F is force in (N), so G results in a value of 6.67 x

10-11

N m2/kg as accurately determined by Load Cavendish.

Test Your Math Skills:

(a) If one of the two masses were to magically double, the force of gravity between the two

bodies at the same separation would

______________________________________________________________________.

(b) If both masses magically double, the force of gravity between the two bodies at the

same separation would

______________________________________________________________________.

(c) If the separation between the same masses would halve, the force of gravity between

the two bodies would

______________________________________________________________________.

(d) If both masses triple and the separation triples, the force of gravity between the two

bodies would

_____________________________________________________________________.

(D) Satellite Circular Motion

If a satellite is to orbit in a circular path around a central mass, only correct physical

quantities will work and be mathematically appropriate. A circular orbit of the earth around

the sun or the moon around the earth come close. A man-made satellite in a circular path

around the earth is possible such as a communication satellite. A sketch is shown for mass

(m) orbiting a large body (M) at a separation (R) and going at the proper velocity (v) to

maintain circular orbit.

v

o m

Fc

M

The force between the two bodies is gravity, which is also a centripetal force; therefore, we

can write:

Force of gravity = Force centripetal

Fg = Fc

GMm = mv2

R2 R

Recall that F = ma and therefore at any point in space above M, Fs = w = mg, thus,

GMm = mv2 = mg

R R

From these formulas and a lot of algebra, one can calculate quantities like “g” at any point

in space, “M,” the mass of the central body, “v,” the orbit velocity to maintain circular

orbit, and “R,” the orbit separation to maintain circular orbit.

Test Your Math Skills:

(a) If you were in an orbiting space ship and wanted to double your velocity, where

in space would you need to go to continue your circular path?

______________________________________________________________________

(b) If R doubles, what happens to “g” at this new location?

______________________________________________________________________

(E) Escape Velocity, Bound and Non-bound Orbits

Gravitational potential energy near earth depends on the mass, acceleration of gravity and

the position of the mass (height above another point). If a 1 kg mass is 1 m above the earth

with g = 9.8 m/s/s, the GPE is “mg # h” equaling (1 kg)(9.8 m/s/s)(1 m) = 9.8 J. However,

GPE is relative, as in this sketch:

2 m

Sketch

0.5 m

1 m

John holds a 1kg mass 0.5 m above a 1-m-tall table in a room that is 3.5 m tall. If one asks

the question, “What is the ball’s GPE?,” it is not a good question, since it doesn’t give the

relative reference point. The following questions are good questions:

(a) What is the mass’s GPE relative to the table? _______________________

(b) What is the mass’s GPE relative to the floor? _______________________

(c) What is the mass’s GPE relative to the ceiling? _______________________

Work was done on the mass to get it above the table and floor, but more work would need

to be done on the mass-earth system (against the gravitational field) to raise it to the

ceiling; thus, the mass is MISSING ENERGY, or -GPE.

GPE is relative. GPE for planetary or satellite motion begins with a definition of 0 energy

at infinity. Since the force of gravity does “work” on falling bodies, the gravitational force

field “looses” energy as two bodies come closer together; the energy becomes NEGATIVE

since the field does the pulling (internal work).

If a ball is thrown above the ground near the earth, the ball-earth system has both kinetic

and gravitational energy to total the following:

ET = KE + GPE

If a satellite is above the earth in an earth-satellite system, the total energy is:

Total Energy = Kinetic Energy + Gravitational Potential Energy

ET = KE + GPE

For the satellite-earth system, a NEGATIVE GPE exists and equals –GmM/R (no proof

offered—calculus is required).

So, ET = ! mv2 - GMm/R.

Three possibilities exist for the total energy of the satellite-central body (earth) system:

1. If KE › GPE, the satellite has so much motion (kinetic) energy that the satellite will

escape with plenty of KE, which illustrates a non-bound system.

2. If KE is ‹ GPE, the satellite cannot escape, like a baseball tossed near the earth, and will

return to the earth showing a bound system.

3. If KE = GPE, the satellite is not bound and can escape the earth, which is called the

escape velocity (what goes up DOESN’T have to come down).

Questions:

(a) How could you calculate “escape velocity” from earth?

__________________________________________________________________________

__________________________________________________________________________

__________________________________________________________________________

(b) What quantities would you need to know to escape from earth?

__________________________________________________________________________

__________________________________________________________________________

__________________________________________________________________________

Topic 8: Gravitational Worksheet Answer Sheet

A. 1. (a) The spray expands. (b) 4

2. 1/4 as much

3. As distance increases, the butter per slice decreases; specifically, the inverse square law

is illustrated.

4. 1/9 as much

1. Same

2. F ! 1/22 = 1/4 as much

3. F ! 1/42 = 1/16

4. Toward the center of the large mass

5. Toward the center of the large mass

6. Acceleration of gravity (g)

7. F = ma, so, w = mg.

8. C

D

A

B. Field 2 is stronger.

(a) Same

(b) 1/9 as much

(c) 1/16 as much

No, at greater distances, the force field approaches 0, but never reaches zero.

The force field inside a mass actually decreases linear from the top surface inward to the

center (requires calculus proof).

C. (a) Double (m is 2x; F is 2x.)

(b) Quadruples (4x) (m1 is 2x, m2 is 2x, so F is 2 x 2 = 4.)

(c) 1/4 (1/2 x 1/2 = 1/4)

(d) (3 m)(3 m) / (3) = 1, or the same.

D. (a) Gm/R2 = mv

2/R v = GM/R For v to double (2 v) while G & M are

constant, R must be 1/4 the original R.

(b) gm = GMm/R2, so, g = GM/R

2. If R doubles, g is 1/4 (1/2

2).

E. (a) mgh = (1 kg)(9.8 m/s/s)(0.5 m) = 4.9 J

(b) mgh = (1 kg)(9.8 m/s/s)(1.5 m) = 14.7 J

(c) mgh = (1 kg)(9.8 m/s/s)(-2 m) = -19.6 J

(a) ET = 1/2 mv2 - GMm/R

Set ET = 0, so 1/2 mv2 = GMm/R v

2 = 2 GM/R.

v = 2 GM/R escape velocity

(b) 1. Universal constant

2. Mass of earth

3. Radius of earth

Topic 8: Demonstration: Up and Down – g

Purpose: To compare “g” going up and “g” going down. Are they the same or different?

Setup: Hand

Fist

Ticker Tape

Board

Ball

Timer Timer

Ball

Power Supply Power Supply

Down Cart Up Cart

Enlargement of Propelling Device: 8”

20”

4”

Procedure:

“g” going down

1. Set up the power supply and mechanical ticker timer on the side of a tall cart near the top

of the cart (see sketch).

2. Test the timer to give consistent and dark carbon dots on a practice ticker tape.

3. Tape a 1 m ticker tape to the baseball. Label the tape “down” and write on the top of the

tape “top” and “bottom” for the end of the tape attached to the ball.

4. Thread the tape upward through the timer so the ball is near the timer (sketch).

5. Hold the tape at the top and hold the tape and ball at rest. Start the timer.

6. Drop. Put the tape on a flat table.

“g” going up

1. Make a 1” x 4” x 28” board with a pivot notch about 8” from one end. Create an

indentation for the ball to rest on about 1” from the other end.

2. Set up as shown with the notch in the board resting atop a knife edge made on the top of a

2” x 4” piece of wood.

3. Place a 2” x 4” x 4” wood stop under the 8” end of the board.

4. Tape a 1 m ticker tape to the baseball. Label the tape “up” and also write on the tape

“top” near the ball and “bottom” near the end by the floor.

5. Thread the tape down through the timer (sketch) and pull snug.

6. With the timer on, firmly strike the 8” end of wood downward to the stop. The ball will

fly up and out of the timer.

7. Align this “up” tape next to the “down” tape with top next to top and bottom next to

bottom.

Top Up Bottom

Top Down Bottom

8. Compare about 40 cm from the center sections of the two tapes insuring both tapes are in

free fall.

9. Slide one of the tapes back and forth to see if dots match up. If dots match side by side,

what does this show about “g” going up and down?

Answer:

The dots can be adjusted so they are side by side, showing the value of “g” is the same

going up as down. With up being defined as +, g becomes negative because the ball slows

down (! v is -). With down being defined as “negative,” g is – because ! v is + but the

direction is -.

Johannes Kepler – The Father of Sci-Fi

In his early days at university, Kepler wrote one of his required dissertations in response

to a challenge made by Michael Maestlin, a believer of Copernicus and one of the most

learned astronomers of all time. The subject of the thesis is how phenomena occurring in

the heavens would appear if observed from the moon. The thesis was never published but the

idea led Kepler to write the story, “Somnium” (The Dream), about a man who travels to the

moon and describes his experiences.

Our traveler describes the forces necessary to propel a body against earth’s gravity.

Kepler suggests numbing the body and arranging the limbs so that they will not be torn apart by

the “force of acceleration.” He also warns of the dangers in breathing the extremely cold air in

space. It seems that Kepler could not imagine a vacuum in space. Once free of earth, “the bodily

mass proceeds toward its destination of its own accord. Here Kepler introduces the concept of

inertia. During the journey the traveler must be shielded from deadly solar radiation by traveling

during the lunar eclipse, the earth’s shadow providing the necessary protection.

Kepler recognized that in a dynamic Copernican system, the path traveled from earth to

the moon is not a straight line, but rather a trajectory from earth to a point in space where the

moon and the lunar voyager would arrive simultaneously. Today this path is called a transfer

orbit.

Kepler spent most of his life perfecting “The Dream.” Future writers of cosmic voyages

would find Kepler’s work inspiring. Jules Verne, H. G. Wells and Arthur C. Clark, some of the

greatest science fiction writers of all time, read the Somnium.

Johannes Kepler – Amazing Accomplishments

Johannes Kepler was a man of significant accomplishments. Presented are some of his

notable discoveries.

• First to explain how an image forms in a pinhole camera.

• First to explain the process of image formation in the eye using the concept of

refraction, the bending of light as it passes through a substance.

• First to design eyeglasses for correcting nearsightedness and farsightedness.

• First to explain the use of both eyes to perceive depth.

• First to describe images as real, virtual, upright and inverted.

• First to explain how the magnification results from light passing through a lens.

• First to explain how a telescope works.

• First to design and build an astronomical telescope (two convex lenses).

• First to discover and describe the properties of total internal reflection.

• First to explain how tides are caused by the moon.

• First to use stellar parallax to determine the distance to the fixed stars.

• First to suggest that the sun rotates about its axis.

• First to derive logarithms purely based on mathematics.

• First to use the term “satellite” to describe orbital motion.

• First to discover that light entering a parabolic reflector converges at the focal point

of the parabola.

• First to write a true science fiction story.

• First to discover that the path of Mars is an ellipse.

• First to put forth scientific evidence to dispel Aristotle’s astronomy.

Tycho’s Knows

On the tenth of December 1566, a dance was held at Lucas Bacmeister’s house in

preparation for a wedding. Lucas Bacmeister was a professor of theology at the University of

Rostock where Tycho studied. Among the guests were nineteen-year-old Tycho Brahe and

another Danish nobleman, Mauderup Parsberg. An argument erupted and they separated in

anger. Several weeks later on December 27, the argument started again.

It seems that Brahe and Parsberg had competed in studying mathematics and other higher

sciences. Apparently the quarrel centered on who was the more skilled mathematician and, in the

evening of December 29, tempers flared and a duel was held. The two men, armed with rapiers,

faced each other at 7 P.M. in total darkness. The duel ended with Parsberg cutting Tycho on the

bridge of his nose. In this encounter Tycho lost the front part of his nose. Tycho had an artificial

nose made, not from wax but from an alloy of gold and silver and put it on so skillfully that it

looked like a real nose. A close friend of Brahe is reported to have said that Tycho used to carry

a small box with a paste, with which he would often “put on the nose.”

Tycho’s grave was opened on June 24, 1901 on the three-hundredth anniversary of his

death. On the front of his cranium there were clear green marks. Evidently the metal piece of his

artificial nose must have had a significant amount of copper also. The hostility between Tycho

and Parsberg however was not lasting, and Parsberg became one of Tycho’s greatest supporters

under the Danish king, Christian IV.

Tycho’s Pet Moose

A famous story about Tycho Brahe is about his tame pet moose. Tycho had extensive

mail correspondence with Lantgrave Wilhelm of Kassel in Germany about astronomical events.

In 1591 Lantgrave wrote to Brahe about an animal he had heard about called “Rix,” which was

faster than a deer but had smaller horns. Tycho replied that such an animal did not exist, but

maybe he meant the Norwegian animal called reindeer. He also wrote that he would check about

such animals and if he could perhaps send one. Tycho added that he had a young moose so tame

that the moose would follow him like a dog and that he would send it if Lantgrave so desired.

Lantgrave replied that he had reindeers before but that they died in the heat. But he would

gladly accept a tame moose and would reward Tycho with a fine riding horse for his efforts. In

the meantime, Tycho had loaned out his pet moose to entertain a group of noblemen in the castle

of Landskrona in a nearby city.

It seems that during the dinner the moose had wandered upstairs and had gotten into the

castle’s store of beer. The moose had drunk so muck beer that he became drunk, fell down the

stairs and broke a leg. Despite the best care, the moose died shortly thereafter. Tycho then wrote

to Lantgrave explaining the problem and said that he would be glad to order another moose.

Nicolas Copernicus

Nicolas Copernicus was born in northern Poland in 1473. At the age of ten his father had

died and the church became his home. Nicolas was appointed canon at age 24 and held that

position until he died in 1543. He studied mathematics, astronomy, medicine, church law and

painting. The picture typically associated with Copernicus is a self-portrait. He lived in the time

of Michelangelo, Leonardo da Vinci, Gerrard Mercator and Christopher Columbus. Copernicus

was truly a renaissance man.

Copernicus became interested in the fact that, since its beginning, the Julian calendar,

instituted in 45 B.C., showed a difference of ten days between the predicted and the actual spring

equinox. He turned to Ptolemy’s Almagest only to find it complicated and confusing. Ptolemy

had taken Aristotle’s stationary, earth-centered heavens and added a system of epicycles and

deferents to explain planetary motion. As a purely academic and aesthetic exercise, Copernicus

asked the question: “What if”? “What if the stationary earth was replaced by a moving earth”?

How would Ptolemy’s universe change?

The resulting heliocentric system did not replace the epicycle and the deferent, nor did it

fit the observable facts any better. The Copernican system could not predict the position of the

planets with any more accuracy than the Ptolemic system. Copernicus devised no experiment,

collected no data, derived no new mathematics or offered any proof.

The appeal and acceptance of the Copernican system was its simplicity and elegance. The

proofs were left to Tycho Brahe and Johannes Kepler.